Answer: m∠ATC = 54°
Step-by-step explanation:
Ok, we know that:
m∠ATB = 20° and m∠BTD = 72°
then we must have that the angle between A and D, is equal to the sum of the angles between A and B, and B and D, or:
m∠ATD = m∠ATB + m∠BTD = 20° + 72° = 92°
Now, we also know that m∠CTD = 38°
And the angle:
m∠ATC will be equal to the angle between A and D, minus the angle between C and D, or:
m∠ATC = m∠ATD - m∠CTD = 92° - 38° = 54°
A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10sin( t ) N(newtons) and moves in a medium that imparts a viscous force of 2 N
when the speed of the mass is 4 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 3 cm/s, formulate the initial value problem describing the motion of the mass.
A)Find the solution of the initial value problem in the above problem.
B)Plot the graph of the steady state solution
C)If the given external force is replaced by a force of 2 cos(ωt) of frequency ω , find the value of ω for which the amplitude of the forced response is maximum.
Answer:
A) C1 = 0.00187 m = 0.187 cm, C2 = 0.0062 m = 0.62 cm
B) A sample of how the graph looks like is attached below ( periodic sine wave )
C) w = [tex]\sqrt[4]{3}[/tex] is when the amplitude of the forced response is maximum
Step-by-step explanation:
Given data :
mass = 5kg
length of spring = 10 cm = 0.1 m
f(t) = 10sin(t) N
viscous force = 2 N
speed of mass = 4 cm/s = 0.04 m/s
initial velocity = 3 cm/s = 0.03 m/s
Formulating initial value problem
y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m
spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m
f(t) = 10sin(t/2) N
using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion
the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)
A) finding the solution of the initial value
attached below is the solution and
B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like
C attached below
The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 6.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 6.0 minutes.
Answer: P(X<6) = 0.3085 or 30.85%
Step-by-step explanation: Determine, first, z-score:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
x is a random variable for time a student takes to find a spot, in this case, x=6:
[tex]z = \frac{6-6.5}{1}[/tex]
z = -0.5
Using z-score table, find z-score:
P(X<6) = P(z< -0.5)
P(X<6) = 0.3085
Probability of finding a parking spot in less than 6 minutes is approximately 30.85%.
Given these four points: A(3, 3), B(−5, 7), C(2, 11), and D(9, −2), find the coordinates of the midpoint of line segments AB and CD.
Midpoint formula: (x1 + x2)/2 , (y1 + y2)/2
Midpoint AB = (3 +-5)/2, (3 + 7)/2 = -2/2 , 10/2 = (-1,5)
Midpoint CD = (2 +9)/2, (11 + -2)/2 = (11/2,9/2)
True or false? The polynomial 3xy + 4z - 8 is a trinomial.
Answer:
False is the answer.Step-by-step explanation:
answer is False.Answer:
True.
Step-by-step explanation:
A trinomial is an algebraic expression consisting of 3 terms. The terms in this instance are: 3xy, 4z, and -8.
In a factory there are 100 units of a certain product, 5 of which are defective. We pick three units from the 100 units at random. What is the probability that none of them are defective
Answer:
Probability of picking all three non-defective units
= 7372/8085 (or 0.911812 to six decimals)
Step-by-step explanation:
Let
D = event that the picked unit is defective
N = event that the picked unit is not defective
Pick are without replacement.
We need to calculate P(NNN) using the multiplication rule,
P(NNN)
= 97/100 * 96/99 * 95/98
=7372/8085
= 0.97*0.969697*0.9693878
= 0.911812
The probability that none of the picked products are defective is;
P(None picked is defective) = 0.856
We are told that 5 are defective out of 100.This means the number of good products that are not defective are 95.
Probability of the first picked product not being defective is written as; P(First picked not defective) = 95/100Since the good ones have been picked, there will be 99 left of which the good ones are now 94. Thus, probability of second one not being defective = 94/99Since two good ones have been picked, there will be 98 left and 93 good ones left. Thus, probability of third one not being defective = 93/98Finally, Probability of none of the three being defective is;95/100 × 94/99 × 93/98 = 0.856
Read more at; https://brainly.com/question/14661097
what is the least common denominator of 1/8, 2/9, and 3/12
A. 864
B. 108
C. 72
D. 48
Answer:
c. 72
Step-by-step explanation:
you just have to see what is the lowest number the three denominators: 8, 9, 12, all go into
8 times 9=72 and 12 times 6=72, which makes answer choice C. &2 the least common denominator for the fractions 1/8, 2/9, and 3/12.
Answer:
c.72 he's right love you guys byeee you all welcome
Step-by-step explanation:
Determine the slope of the line passing through the points (0,-3) and (3,-11).
Answer:
-3/8
Step-by-step explanation:
Hey there!
Well to find the slope with 2 points “(0,-3) and (3,-11)”, we’ll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
Plug in the given points.
[tex]\frac{-11 - - 3}{3-0}[/tex]
-11 + 3 = -8
3 - 0 = 3
Slope = -8/3
Hope this helps :)
What is the name of a geometric figure that looks an orange
A. Cube
B. Sphere
C. Cylinder
D. Cone
Answer:
b . sphere
Step-by-step explanation:
On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point could be on the line that is parallel to line KL and passes through point M? (–10, 0) (–6, 2) (0, –6) (8, –10)
Answer:
The point that lies on the line parallel to line KL would be ( 8, - 10 )
Step-by-step explanation:
Line KL passes through the points ( - 6, 8 ) and ( 6, 0 ) while it's respective parallel line passes through point M, ( - 4, - 2 ).
Our approach here is to first determine the slope of KL such that the slope of it's parallel line will be the same, and hence we can determine a second point on this line.
Slope of KL : ( y₂ - y₁ ) / ( x₂ - x₁ ),
( 0 - 8 ) / ( 6 - ( - 6 ) ) = - 8 / 6 + 6 = - 8 / 12 = - 2 / 3
Slope of respective Parallel line : - 2 / 3,
Another point on Parallel line : ( 8, - 10 )
How can we check if this point really belongs to the parallel line? Let's take the slope given the points ( - 4, - 2 ) and ( 8, - 10 ), and check if it is - 2 / 3.
( y₂ - y₁ ) / ( x₂ - x₁ ),
( - 10 - ( - 2 ) ) / ( 8 - ( - 4 ) ) = ( - 10 + 2 ) / ( 8 + 4 ) = - 8 / 12 = - 2 / 3
And therefore we can confirm that this point belongs to line KL's parallel line, that passes through point M.
Answer:
D
Step-by-step explanation:
12.5% of it is 6 hrs
Answer:
48 hours
Step-by-step explanation:
12.5/100 = 6/x
1. cross-multiply
12.5 × x = 12.5x
100 × 6 = 600
2. divide
12.5x/12.5 = x
600/12.5 = 48
3. answer
x = 48
A mail truck traveled 82 miles in 4 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?
Answer:
= 18.2 miles per hour
Step-by-step explanation:
Speed = distance / time
=82 miles / 4.5 hours
=18.22222222 miles per hour
Rounding
= 18.2 miles per hour
Answer:
Given that
Distance = rate × time
82 = r × 4½
r = 18.2 mph
Select the correct answer from each drop-down menu.
The table represents function f, and the graph represents function g.
-2
- 1
1
2
3
4
0
х
Ax)
7
0
-5
-8
-9
-8
-5
у
A
6
4
2
g
X
.
-21
2
2
The line of symmetry for function fis
and the line of symmetry for function gis
The y-intercept of function fis
the y-intercept of function g.
Over the interval [2, 4], the average rate of change of function fis
the average rate of change of function g.
Answer:
Line of symmetry of f is x=2 and the line of symmetry for function g is x=1 as the graph starts repeating itself after x=1. Y intercept is the point at which x is 0, for f it is - 5 and for g it is - 6. Rate of change in interval [2,4] is given by (f(4)-f(2))/2=2 for f and for g it is, (g(4)-g(2))/2=-4
The true statements are:
The line of symmetry for function f is x = 2The line of symmetry for function g is x = 1The y-intercept of function f is -5The y-intercept of function g is -6Over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.Line of SymmetryThis is the point where the function is divided into equal halves.
From the figure, the table and graph are divided at points x = 2, and x = 1.
So, the line of symmetry for function f is x = 2 and the line of symmetry for function g is x = 1
Y-InterceptThis is the point where the function has an x value of 0
From the figure, the y values when x = 0 are -5 and -6
So, the y-intercept of function f is -5 and the y-intercept of function g is -6
Average rate of changeThis is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
For function f, we have:
[tex]m = \frac{-5 + 9}{4-2}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m = 2[/tex]
For function g, we have:
[tex]m = \frac{2+ 6}{4-2}[/tex]
[tex]m = \frac{8}{2}[/tex]
[tex]m = 4[/tex]
By comparison,
[tex]m_f = 0.5 \times m_g[/tex]
Hence, over the interval [2, 4], the average rate of change of function f is half the average rate of change of function g.
Read more about functions and graphs at:
https://brainly.com/question/13136492
Theresa bought 2 pineapples for $6. She wants to find the constant of proportionality in terms of dollars per pineapple. She modeled this proportional relationship on a number line diagram, as shown.
Part B
How much would 4 pineapples cost?
The yellow bar is the total cost of 2 pineapples. The black line in the middle of the yellow splits it equally in half and is located at the 3.
The constant bod proportionality would be 3, which means each pineapple cost $3
Answer:
first of all, brainly better not delete my answer again. (the answer is 3)
Step-by-step explanation:
you have to multiply to find the number of pineapples. but unlike me i did skip count and write down my number's and I tried to find "what number skips until it ends to 6?'' i found 3 as my answer! 3,6,9,12,15,18,21 etc..
HELPP plz don't send a file whats the answer and explanation plz if you can
Answer:
5/0 is not a rational number
Step-by-step explanation:
you cant divide by 0
What is the equation of the following graph?
Answer:
y=0.5x + 5
Step-by-step explanation:
The points are (0,5) and (-10,0)
to find the slope do
0-5/-10-0 = 5/10 = 1/2 = 0.5
next plug one of the points into point slope formula
y-y1=m(x-x1)
lets use the point (-10,0)
y1=0
x1= -10
m= 0.5
y-0=0.5(x- -10)
y = 0.5(x+10)
distribute the 0.5
y=0.5x+5
8) The perimeter of a rectangle is 20x2 + xy - 7y2 and one of it's sides is
7x2 - xy. Find the other side.
Answer:
3x^2 + 3xy/2 - 7xy^2/2
Step-by-step explanation:
So we know the perimeter is 20x^2 + xy - 7y^2,
To find any perimeter you need 2l + 2w = P so,
One of the sides is 7x^2 - xy
First plug in the values,
2(7x^2-xy) + 2w = 20x^2 + xy - 7y^2
Multiply,
14x^2-2xy + 2w = 20x^2 + xy - 7y^2
Subtract,
14x^2 - 2xy - 14x^2 + 2xy + 2w = 20x^2 + xy - 7y^2 - 14x^2 + 2xy
2w = 6x^2 + 3xy - 7y^2
w = 3x^2 + 3xy/2 - 7xy^2/2
Nour drove from the Dead Sea up to Amman, and her altitude changed at a constant rate. When she began driving, her altitude was 400400400 meters below sea level. When she arrived in Amman 222 hours later, her altitude was 100010001000 meters above sea level. Let yyy represent Nour's altitude (in meters) relative to sea level after xxx hours.
Answer:
y = 700x - 400
Step-by-step explanation:
A negative number represents an altitude below sea level.
Beginning: -400
y = mx + b
y = mx - 400
In 2 hours the altitude was now 1000 m.
1000 m - (400 m) = 1400 m
The altitude went up 1400 m in 2 hours. The rate of change is
1400/2 m/h = 700 m/h
The rate of change is the slope.
y = 700x - 400
Answer:
The graph answer is below :)
Step-by-step explanation:
Plzz help i really need help..
Answer:
D. neither.
Step-by-step explanation:
A function is when one x-value only has one corrisponding y-value.
The answer it's D. Neither
If X = 4 and y = -2, the value of 1/2 xy^2 is
Answer:
[tex]8[/tex]
Step-by-step explanation:
Note that 1/2 xy^2 is, by order of operations, read as [tex]\frac12xy^2[/tex]. If this is not what was intended in the question then please amend it according order of operations.
Plugging the values [tex]x=4[/tex] and [tex]y=-2[/tex] gives
[tex]\frac12xy^2=\frac12(4)(-2)^2=\frac12(4)(4)=\frac12(16)=8[/tex]
HELP ME PLEASE 10 POINTS SCIENTIFIC NOTATION
2,100,000.
Move the decimal point six places to the right spawning zeros. You will get 2million 100k.
If exponents get negative move the decimal point to the left spawning zeros in front.
Hope this helps :)
Find the interquartile range of the following data set.
Number of Points Scored at Ten Basketball Games
57 63 44 29 36 62 48 50 42 34
A.21
B.28
C.6
D.34
Answer:
[tex]\huge\boxed{IQR = 21}[/tex]
Step-by-step explanation:
The data set given is:
57,63,44,29,36,62,48,50,42,34
Arrange in ascending order:
29,34,36,42,44,48,50,57,62,63
Place parenthesis around the number making two equal sets.
(29,34,36,42,44) | (48,50,57,62,63)
↑ ↑
Q1 Q3
Q1 = 36 , Q3 = 57
So, IQR = Q3-Q1
IQR = 57-36
IQR = 21
Answer:
[tex]\huge \boxed{\sf A. \ 21}[/tex]
Step-by-step explanation:
The data set is given,
[tex]\sf 57 \ 63 \ 44 \ 29 \ 36 \ 62 \ 48 \ 50 \ 42 \ 34[/tex]
Arrange the data set in ascending order.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Split the data set into two equal sets.
[tex]\sf 29 \ 34 \ 36 \ 42 \ 44 \ \ \ 48 \ 50 \ 57 \ 62 \ 63[/tex]
Find the median of the lower half and upper half.
[tex]\sf Median \ of \ lower \ half = 36[/tex]
[tex]\sf Median \ of \ upper \ half = 57[/tex]
Interquartile range = median of upper half - median of lower half
[tex]\sf IQR = 57 - 36[/tex]
[tex]\sf IQR = 21[/tex]
The interquartile range for the number of points scored at ten basketball games is 21.
please help give bralienst not need explation
Answer:
4.5 cm
Step-by-step explanation:
The ruler says it all..... (why do you need help with this? What grade????)
Hope this helps, have a good day :)
Answer:Its 4.5 centimeters
Step-by-step explanation:
Help me plz need the steps
In Figure 7 (open photo), GH is a diameter of the circle. What is
x² + y² ?
A)58
(B) 49
(C) 10
D) 9
(E) It cannot be determined from the information given.
Answer:
[tex]A)58[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ attachment]\\We\ are\ given:\\GH\ is\ the\ diameter\ of\ the\ circle.\\ Also,\\ GM=3\ units\ and\ MH=7\ units\\From\ the\ figure,\\GH\ subtends\ an\ angle\ at\ two\ points\ specifically\ M\ and\ N\ on\ the\\ arc.\\Now,\\We\ know\ that,\\'The\ Angle\ subtended\ by\ the\ diameter\ anywhere\ over\ the\ arc\ of\ the\\ circle\ is\ always\ 90\ degrees'.\\Hence,\\\angle GMH\ = \angle GNH=90\\[/tex]
[tex]Also,\\Pythagoras\ Theorem\ states\ that: 'In\ a\ right\ triangle,\ the\ sum\ of\ squares\\ \ of\ the\ legs\ is\ equal\ to\ the\ square\ of\ the\ hypotenuse'\\In\ \triangle GMH,\\Since\ \angle GMH=90,\\GM^2+MH^2=GH^2[Through\ Pythagoras\ Theorem]\\Hence,\\Substituting\ GM=3,\ MH=7:\\3^2+7^2=GH^2\\GH^2=9+49=58[/tex]
[tex]Similarly,\\In\ \triangle GNH,\\Since\ \angle GNH=90,\\GN^2+NH^2=GH^2\\Hence,\\Substituting\ GN=x\ and\ NH=y:\\x^2+y^2=GH^2\\x^2+y^2=58[/tex]
find the area of the circle use 3.14 for pi d=4 m
Answer:
The area of circle is 12.56m sq.
Evaluate x^2 − 4x + 5, when x = − 3
Answer:
[tex]\huge\boxed{26}[/tex]
Step-by-step explanation:
[tex]\sf x^2-4x+5\\Given \ that \ x = -3\\(-3)^2-4(-3)+5\\9+12+5\\26[/tex]
Answer:
[tex] \boxed{26}[/tex]
Step-by-step explanation:
[tex] \mathsf{ {x}^{2} - 4x + 5}[/tex]
[tex] \mathrm{Plug \: the \: value \: of \: x}[/tex]
⇒[tex] {( - 3)}^{2} - 4 \times(- 3 )+ 5[/tex]
[tex] \mathrm{Evaluate \: the \: power}[/tex]
⇒[tex] \mathsf{9 - 4 \times(- 3 ) + 5}[/tex]
[tex] \mathrm{Multiply \: the \: numbers}[/tex]
⇒[tex] \mathsf{9 + 12 + 5}[/tex]
[tex] \mathrm{Add the numbers}[/tex]
⇒[tex] \mathsf{26}[/tex]
Hope I helped!
Best regards!
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 250,823. Its current population is 325,823. By about what percentage has the city grown over the past ten years? Round to the nearest percent.
Answer:
I just answered it
Step-by-step explanation:
Solve for x . 7 - (2 x + 11) + 3(3 - x ) = 20
A.7/5
B.-3
C.-4
Answer:
the answer to the question is a:-3
(05.06A LC)
Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B'. What is the length
of A'B'?
1 unit
4 units
5 units
6 units
Answer:
4 units
Step-by-step explanation:
A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.
If a shape is transformed, the length of its sides and shape remains the same, only the position changes.
If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:
Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:
[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:
[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
AB = A'B' = 4 units
At the age of 10, Edgar received an inheritance of $10,000. His father wants to invest the money in an account that will double in value in 8 years. Approximately what interest rate does the father need to find in order to reach his goal?
Answer:
9%
Step-by-step explanation:
Use the rule of 72. If you want the money to double in 8 years, it will need to be at 9 percent interest rate to reach this goal.
WILL GIVE BRAINLIEST!!!
f(x) = 2/cos 2x
f(x) = 2/sin1x
f(x)=1/cos1/sin3
{x∣x ≠ π/4+πn/2} , for any integer n
Must click thanks and mark brainliest